Calculate the amount of heat needed to melt 69.7 g of solid hexane (C6H14) and bring it to a temperature of 47.2 degrees Celsius. Round your answer to three significant digits and include a unit symbol in your answer
To calculate the amount of heat needed to melt the solid hexane and raise its temperature, we need to consider two separate processes: the heat needed to melt the hexane and the heat needed to raise its temperature.
1. Heat needed to melt the hexane:
The heat of fusion, or the amount of heat required to melt 1 gram of a substance, for hexane is 9.95 kJ/mol. We can convert grams to moles using the molar mass of hexane:
Molar mass of C6H14 = (6 * 12.01 g/mol) + (14 * 1.01 g/mol) = 86.18 g/mol
So, the number of moles of hexane is:
Moles of hexane = 69.7 g / 86.18 g/mol = 0.8081 mol
The heat needed to melt the hexane is then given by:
Heat = Moles of hexane * Heat of fusion
Heat = 0.8081 mol * 9.95 kJ/mol = 8.042 kJ
2. Heat needed to raise the temperature:
The specific heat capacity of hexane is 2.21 J/g°C.
The temperature change is given as 47.2°C, so we need to multiply it by the mass of hexane:
Heat = Mass of hexane * Specific heat capacity * Temperature change
Heat = 69.7 g * 2.21 J/g°C * 47.2°C = 7262.06 J
Converting J to kJ:
Heat = 7262.06 J / 1000 = 7.2621 kJ
Now, we can find the total heat needed by adding the heat required for melting and the heat required for raising the temperature:
Total heat = Heat for melting + Heat for raising the temperature
Total heat = 8.042 kJ + 7.2621 kJ = 15.3041 kJ
Rounded to three significant digits:
Total heat = 15.3 kJ